Regions representing objects are called "figures" while "ground" typically refers to regions representing the background of the objects. An important difference between figures and ground is that the figure always has shape while the ground may not have shape. This difference is particularly obvious with natural 3D scenes. A 3D shape of an object does not change when an observer changes his viewing position or when the object is translated and rotated in the 3D space. This is different with 3D background whose geometry (and thus shape) changes when objects move relative to each other. Ability to see 3D shape as the same regardless of the viewing direction is called shape constancy. Can shape constancy be achieved with 3D empty space? We tested human performance in a shape constancy task with a 3D symmetrical rigid "object" and a 3D asymmetrical rigid empty "space". The subject memorized 3D shapes of two test stimuli in the first display and judged whether either of them was identical with the 3D shape of a response stimulus in the second display. The 3D shape of the response stimulus was rotated in depth by 15, 45 and 75 deg angles. The stimuli were viewed binocularly. In "object" condition, the stimulus was perceived as a 3D "polyhedron". In "space" condition, the stimulus was perceived as a 3D curve surrounding space between two polyhedral objects. The results show that the performance with "object" is substantially better than with "space". When the stimuli are shown in isolation (figure without ground or ground without figure), performance improves, especially in the "space" condition. This means that the visual system has the ability to extract the shape of a 3D rigid space between objects, but when objects are present they draw attention as figures away from ground.